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The area of the region bounded by the curves x(1 + y²) = 1 and y² = 2x is:

1. 2 ((π)/(2)-(1)/(3))
2. (π)/(4)-(1)/(3)
3. (π)/(2)-(1)/(3)
4. (1)/(2) ((π)/(2)-(1)/(3))

Correct answer: (π)/(2)-(1)/(3)

Solution

The correct option is right because it accurately represents the area calculated between the two curves, where the integration of the bounded region yields the result of /2(/2-/3) after evaluating the definite integrals and applying the appropriate limits.

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